3x(x-6)=5x+20

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Solution for 3x(x-6)=5x+20 equation:


Simplifying
3x(x + -6) = 5x + 20

Reorder the terms:
3x(-6 + x) = 5x + 20
(-6 * 3x + x * 3x) = 5x + 20
(-18x + 3x2) = 5x + 20

Reorder the terms:
-18x + 3x2 = 20 + 5x

Solving
-18x + 3x2 = 20 + 5x

Solving for variable 'x'.

Reorder the terms:
-20 + -18x + -5x + 3x2 = 20 + 5x + -20 + -5x

Combine like terms: -18x + -5x = -23x
-20 + -23x + 3x2 = 20 + 5x + -20 + -5x

Reorder the terms:
-20 + -23x + 3x2 = 20 + -20 + 5x + -5x

Combine like terms: 20 + -20 = 0
-20 + -23x + 3x2 = 0 + 5x + -5x
-20 + -23x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-20 + -23x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-6.666666667 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -7.666666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -7.666666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -7.666666667x + x2 = 0 + 6.666666667
-7.666666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-7.666666667x + x2 = 6.666666667

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = 6.666666667 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = 6.666666667 + 14.69444445

Combine like terms: 6.666666667 + 14.69444445 = 21.361111117
14.69444445 + -7.666666667x + x2 = 21.361111117

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 21.361111117

Calculate the square root of the right side: 4.621808209

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 4.621808209 and -4.621808209.

Subproblem 1

x + -3.833333334 = 4.621808209 Simplifying x + -3.833333334 = 4.621808209 Reorder the terms: -3.833333334 + x = 4.621808209 Solving -3.833333334 + x = 4.621808209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.621808209 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.621808209 + 3.833333334 x = 4.621808209 + 3.833333334 Combine like terms: 4.621808209 + 3.833333334 = 8.455141543 x = 8.455141543 Simplifying x = 8.455141543

Subproblem 2

x + -3.833333334 = -4.621808209 Simplifying x + -3.833333334 = -4.621808209 Reorder the terms: -3.833333334 + x = -4.621808209 Solving -3.833333334 + x = -4.621808209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.621808209 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.621808209 + 3.833333334 x = -4.621808209 + 3.833333334 Combine like terms: -4.621808209 + 3.833333334 = -0.788474875 x = -0.788474875 Simplifying x = -0.788474875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.455141543, -0.788474875}

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